<!DOCTYPE html>
<html lang="en-US">
<!--********************************************-->
<!--*       Generated from PreTeXt source      *-->
<!--*                                          *-->
<!--*         https://pretextbook.org          *-->
<!--*                                          *-->
<!--********************************************-->
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<meta name="robots" content="noindex, nofollow">
</head>
<body class="ignore-math">
<h4 class="heading"><span class="type">Paragraph</span></h4>
<p>The problem in the examples below represents the dynamics of a point, initially at rest, moving away from the origin along the <span class="process-math">\(y\)</span>-axis under a constant acceleration of value <span class="process-math">\(10\)</span> for <span class="process-math">\(0\leq t
&lt;1\)</span> and an extra impulse acceleration of size <span class="process-math">\(10\)</span> is applied at <span class="process-math">\(t=1.\)</span> This is like a simple rocket boost, but can you solve it any other way? We use the Dirac impulse function <span class="process-math">\(\delta(t-a)\)</span> which is nonzero at <span class="process-math">\(t=a,\)</span> but zero elsewhere while having unit total area under it:</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
\delta(t-a)=0 \ {\rm if} \ (t\neq a) \ \
{\rm and} \ \int_{-\infty}^{\infty} \delta(t-a) \, dt = 1.
\end{equation*}
</div>
<span class="incontext"><a href="sec8_5.html#p-493" class="internal">in-context</a></span>
</body>
</html>
